Blame Richard Nixon. That’s the satirical thrust of X-Men: Days of Future Past, an enjoyably convoluted time-travel adventure that takes place mostly in a mildly anachronistic 1973, after the end of the Vietnam War and before Watergate, with the President trying to figure out what to do about America’s potentially insurgent mutant population. Convinced by ambitious scientist Bolivar Trask (Peter Dinklage) that the solution to the problem is to green-light a line of mutant-targeting drones called Sentinels, Tricky Dick acts with predictably self-serving expediency – and inadvertently triggers a series of events that leads to a dystopian future in which humans and mutants alike teeter on the verge of extinction.

It’s in this greyed-out, apocalyptic scenario that Bryan Singer’s film lays out its basic plot line: with their backs against the wall in the present tense, the X-Men (or what’s left of them following a series of Sentinel raids) opt to send Wolverine (Hugh Jackman) – or at least his consciousness – back in time 50 years so that his younger self can try to alter this chronology – a scheme that nods to H.G. Wells and Harlan Ellison (as well as the X-Men comics series). The plot details here are so ludicrous and complicated that you’d need some really good actors to put them across, and luckily Days of Future Past has two fine ensembles at its disposal: not only Jackman and the original X-Men cohort (including Patrick Stewart and Ian McKellen) but also the sleeker, more contemporary models last seen in the mediocre prequel X-Men: First Class.

The big news since that film’s release in the summer of 2011 is that Jennifer Lawrence has gone on to become the biggest movie star in the free world, and so Days of Future Past has upped her role. Her shape-shifting Mystique has gone from an alienated outsider to a would-be assassin whose actions will dictate the whole of human history.

Wolverine’s mission is to convince the younger versions of Professor X (James McAvoy) and Magneto (Michael Fassbender) to help him stop Mystique from murdering Trask (and inflaming anti-mutant hysteria), and Jackman is in fine form bouncing off his pedigreed co-stars: His scenes with McAvoy replicate his tender rapport with Stewart in the early instalments. And Fassbender is reliably fabulous, fully inhabiting Magneto’s arrogance and ambivalence (it’s a compliment to say that as played the character might convincingly age into Ian McKellen).

Unfortunately, Lawrence doesn’t register as strongly, which partially has to do with her role’s malleable particulars (Mystique spends a lot of time being other people) and also her status in the storyline – as both the hunter and the hunted, she spends most of her time in motion and doesn’t get too many character moments. That’s also true of the film as a whole, which is so elaborately plotted – crosscutting between past and future while keeping a good half-dozen subplots spinning in the air – as to seem more like a contraption than a movie.

Having already directed the first two (and superior) X-Men films, Singer shows a level of comfort with both the material and the cast, and he contributes at least one brilliant comic set piece in which new mutant Quicksilver (Evan Peters) lays waste to a kitchen full of security guards in languorous, Matrix-style bullet time (it looks gorgeous and has the slapstick choreography of a Three Stooges routine). Simon Kinberg’s script is awash in banal, expository dialogue – the characters having to keep explaining the plot to each other – but people don’t go to X-Men movies for naturalistic exchanges: a few pithy one-liners will suffice, and Jackman puts the ones he does get across with the gruff brio of an old pro. (Among the film’s principals Wolverine alone suffers the torment of having his consciousness exist in two time frames at once, but the actor seems to be having fun).

Like Captain America: The Winter Soldier and Godzilla, Days of Future Past tries to use real-world history and iconography to prop up its storyline, and while its allusions aren’t particularly deep, the attempts at contextualizing its fantastical action at least evince a little bit of ambition. It doesn’t take a lot of wit or imagination to use Richard Nixon as a bad guy, but it’s still satisfying to watch a climatic showdown between two supervillains – one brought back from out of the past and the other from off the comic-book page – and wait to see who blinks first. Seems like we’ll always have Nixon to kick around, after all.